21 research outputs found
Effective action for the field equations of charged black holes
In this article, we consistently reduce the equations of motion for the
bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for
the metric. This reduction is done in a general, non-supersymmetric setup, in
which we extend concepts of BPS black hole technology. First of all we obtain a
more general form of the black hole potential, as part of an effective action
for both the scalars and the vectors in the supergravity theory. Furthermore,
we show that there are extra constraints specifying the solution, which we
calculate explicitly. In the literature, these constraints have already been
studied in the one-center case. We also show that the effective action we
obtain for non-static metrics, can be linked to the "entropy function" for the
spherically symmetric case, as defined by Sen and Cardoso et al.Comment: 18 pages, (v2: small corrections, version to be published in CQG
Attractor Flows from Defect Lines
Deforming a two dimensional conformal field theory on one side of a trivial
defect line gives rise to a defect separating the original theory from its
deformation. The Casimir force between these defects and other defect lines or
boundaries is used to construct flows on bulk moduli spaces of CFTs. It turns
out, that these flows are constant reparametrizations of gradient flows of the
g-functions of the chosen defect or boundary condition. The special flows
associated to supersymmetric boundary conditions in N=(2,2) superconformal
field theories agree with the attractor flows studied in the context of black
holes in N=2 supergravity.Comment: 28 page
The Kahler Cone as Cosmic Censor
M-theory effects prevent five-dimensional domain-wall and black-hole
solutions from developing curvature singularities. While so far this analysis
was performed for particular models, we now present a model-independent proof
that these solutions do not have naked singularities as long as the Kahler
moduli take values inside the extended Kahler cone. As a by-product we obtain
information on the regularity of the Kahler-cone metric at boundaries of the
Kahler cone and derive relations between the geometry of moduli space and
space-time.Comment: 21 pages, 1 figure. Improved discussion of the relation between
Kahler moduli and five-dimensional scalars. No changes in the conclusion
Building a Better Racetrack
We find IIb compactifications on Calabi-Yau orientifolds in which all Kahler
moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and
Trivedi.Comment: 47 pages, 1 figure, harvmac (v2: added references, minor comments,
v3: improved discussion of metastability and explicit flux vacua
Massless black holes and black rings as effective geometries of the D1-D5 system
We compute correlation functions in the AdS/CFT correspondence to study the
emergence of effective spacetime geometries describing complex underlying
microstates. The basic argument is that almost all microstates of fixed charges
lie close to certain "typical" configurations. These give a universal response
to generic probes, which is captured by an emergent geometry. The details of
the microstates can only be observed by atypical probes. We compute two point
functions in typical ground states of the Ramond sector of the D1-D5 CFT, and
compare with bulk two-point functions computed in asymptotically AdS_3
geometries. For large central charge (which leads to a good semiclassical
limit), and sufficiently small time separation, a typical Ramond ground state
of vanishing R-charge has the M=0 BTZ black hole as its effective description.
At large time separation this effective description breaks down. The CFT
correlators we compute take over, and give a response whose details depend on
the microstate. We also discuss typical states with nonzero R-charge, and argue
that the effective geometry should be a singular black ring. Our results
support the argument that a black hole geometry should be understood as an
effective coarse-grained description that accurately describes the results of
certain typical measurements, but breaks down in general.Comment: 47 pages, 4 figures. v2: references added. v3: minor corrections to
Appendix A, references adde
Non-supersymmetric Black Holes and Topological Strings
We study non-supersymmetric, extremal 4 dimensional black holes which arise
upon compactification of type II superstrings on Calabi-Yau threefolds. We
propose a generalization of the OSV conjecture for higher derivative
corrections to the non-supersymmetric black hole entropy, in terms of the one
parameter refinement of topological string introduced by Nekrasov. We also
study the attractor mechanism for non-supersymmetric black holes and show how
the inverse problem of fixing charges in terms of the attractor value of CY
moduli can be explicitly solved.Comment: 47 pages, harvmac. v2: footnote(4) expanded, references adde
Black Holes as Effective Geometries
Gravitational entropy arises in string theory via coarse graining over an
underlying space of microstates. In this review we would like to address the
question of how the classical black hole geometry itself arises as an effective
or approximate description of a pure state, in a closed string theory, which
semiclassical observers are unable to distinguish from the "naive" geometry. In
cases with enough supersymmetry it has been possible to explicitly construct
these microstates in spacetime, and understand how coarse-graining of
non-singular, horizon-free objects can lead to an effective description as an
extremal black hole. We discuss how these results arise for examples in Type II
string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8
supercharges respectively. For such a picture of black holes as effective
geometries to extend to cases with finite horizon area the scale of quantum
effects in gravity would have to extend well beyond the vicinity of the
singularities in the effective theory. By studying examples in M-theory on
AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.Comment: Review based on lectures of JdB at CERN RTN Winter School and of VB
at PIMS Summer School. 68 pages. Added reference
Wall-Crossing in Coupled 2d-4d Systems
We introduce a new wall-crossing formula which combines and generalizes the
Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d
systems respectively. This 2d-4d wall-crossing formula governs the
wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to
a supersymmetric surface defect. When the theory and defect are compactified on
a circle, we get a 3d theory with a supersymmetric line operator, corresponding
to a hyperholomorphic connection on a vector bundle over a hyperkahler space.
The 2d-4d wall-crossing formula can be interpreted as a smoothness condition
for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can
be determined for 4d theories of class S, that is, for those theories obtained
by compactifying the six-dimensional (0,2) theory with a partial topological
twist on a punctured Riemann surface C. For such theories there are canonical
surface defects. We illustrate with several examples in the case of A_1
theories of class S. Finally, we indicate how our results can be used to
produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure
Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
We survey recent results on quantum corrections to the hypermultiplet moduli
space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or,
equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our
main focus lies on the problem of resumming the infinite series of D-brane and
NS5-brane instantons, using the mathematical machinery of automorphic forms. We
review the proposal that whenever the low-energy theory in D=3 exhibits an
arithmetic "U-duality" symmetry G(Z) the total instanton partition function
arises from a certain unitary automorphic representation of G, whose Fourier
coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1
we argue that the relevant automorphic representation falls in the quaternionic
discrete series of G, and that the partition function can be realized as a
holomorphic section on the twistor space Z over M. We also offer some comments
on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra,
Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201
The Supermembrane with Central Charges on a G2 Manifold
We construct the 11D supermembrane with topological central charges induced
through an irreducible winding on a G2 manifold realized from the T7/Z2xZ2xZ2
orbifold construction. The hamiltonian H of the theory on a T7 target has a
discrete spectrum. Within the discrete symmetries of H associated to large
diffeomorphisms, the Z2xZ2xZ2 group of automorphisms of the quaternionic
subspaces preserving the octonionic structure is relevant. By performing the
corresponding identification on the target space, the supermembrane may be
formulated on a G2 manifold, preserving the discretness of its supersymmetric
spectrum. The corresponding 4D low energy effective field theory has N=1
supersymmetry.Comment: Reviewed version. spectral propertis discussed, two more sections
added, 27 pages,Late